If $f(x)$ is a polynomial function satisfying the condition $f(x) . f(1/x) = f(x) + f(1/x)$ and $f(2) = 9$ then :

Let $A = \{ {x_1},\,{x_2},\,............,{x_7}\} $ and $B = \{ {y_1},\,{y_2},\,{y_3}\} $ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f : A \to B$ that are onto, if there exist exactly three elements $x$ in $A$ such that $f(x)\, = y_2$, is equal to

The mid-point of the domain of the function $f(x)=\sqrt{4-\sqrt{2 x+5}}$ real $x$ is

Let $f, g: N -\{1\} \rightarrow N$ be functions defined by $f(a)=\alpha$, where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^{\alpha}$ divides $a$, and $g(a)=a+1$, for all $a \in N -\{1\}$. Then, the function $f+ g$ is.

If $0 < x < \frac{\pi }{2},$ then

If $x = {\log _2}\left( {\sqrt {56 + \sqrt {56 + \sqrt {56 +  .... + \infty } } } } \right)$ then